A killer in a cagoule? That is the unlikely but alluring prospect held out by Sightseers, a comedy of manners in which murder arrives out of the great blue yonder, usually in the vicinity of a caravan park.

Director Ben Wheatley has in a very short time established himself as an auteur of the domestic macabre, somewhere between Joe Orton and The Wicker Man. This latest isn't as funny as his brilliant debut Down Terrace or as disturbing as his occult thriller, Kill List, but it features many of his signature touches and sets him apart as a film-maker of exceptional talent and daring.

Involved in the writing of the earlier films, Wheatley here directs from an original script by Alice Lowe and Steve Oram, with additional material by his partner Amy Jump. Lowe and Oram also take the lead roles of Tina and Chris, two thirtyish introverts who have just got together.

Tina lives with her needy and spiteful mother (Eileen Davies) who's still mourning, loudly, the death of her pet dog a year ago. And she's appalled at the idea of her daughter going off with Chris for a minibreak: "You don't even know him," she says – with good reason, as it turns out. Chris, genial and ginger, has mapped out their trip from Redditch to the north, and what's more, he has a Volvo with a caravan to transport them.

These early scenes, with their stop-start uncertainty, are possibly the best of the whole film, reminiscent of the glum, bickering couple in Mike Leigh's Nuts in May. Chris has promised Tina "an erotic odyssey", and you can tell just from her packing that she hasn't really a clue what "erotic" might constitute: it certainly isn't her matching knitted bra and pants.

Later, in a restaurant, she whispers to Chris that she isn't wearing any knickers, an effect rather spoilt by the revelation that she is wearing tights. The first sign that Chris might not be the mild-mannered rambler he seems comes when a litter lout deliberately crosses him. He's furious about it, and takes his revenge by "accidentally" reversing his caravan over the offender. As they depart Chris fumes, "He's bloody ruined Crich Tramway Museum for me".

That humdrum reference is a characteristic note in Wheatley. Stopping at a campsite where some hippie types are sacrificing chickens on a hill, Chris is informed that they're "shamans – from Portsmouth, you know".

Such exotica intrigues and baffles the couple. When they meet a middle-class camper named Ian who's writing a book about ley lines, Chris conceives an idea that he will write a book on that theme, too, whether from sudden inspiration or envy isn't clear. He may not have the talent, but he does end up with Ian's camera, and his Scottish terrier. "I just want to be feared and respected," says Chris, and Tina tries to get on his deranged wavelength by joining in the murder spree. But is one caravan enough to contain two undiagnosed psychopaths?

Murder as comedy has a respectable lineage in British cinema, of course. Kind Hearts and Coronets remains Ealing's finest hour, and Hitchcock pushed grisliness and giggliness as close as they ever came in Frenzy, where the rapist-killer happens to be (what else?) a fruit merchant. Sightseers drops hints as to what incites Chris to murder – initially, class-resentment seems to be the trigger, then it turns out to be a more generalised control-freak annoyance.

In Tina, the killer's impulse seems to derive from a quasi-romantic possessiveness, though interestingly her most significant rival for Chris's affections turns out to be another beardy anorak type named Martin, proud inventor of a "carapod" – basically the Sinclair C5 with a bicycle at the front.

In the meantime, the film offers a quirky celebration of English tourist life, from the Ribblehead Viaduct and Fountains Abbey to Mother Shipton's Cave and the Pencil Museum in Keswick. This last venue finds Tina writing Chris an imploring letter with a gigantic novelty pencil, inducing a shiver of The League of Gentlemen. It's not all about poking fun, though. Laurie Rose's cinematography catches the loveliness of the Lake District and Peak District, lingering on those heartstopping stretches of countryside that only the siting of a caravan park could ruin. A green and pleasant land, says the film – just a shame about the people in it.

Sightseers roves and rambles intriguingly, though in the end it doesn't quite deliver on its dark comic premise. The way in which the script pays out revelation is adroitly handled – information about the couple sneaks out in sidelong moments, the best of them a stand-alone sequence that might be titled "The Dog It Was That Died". And in identifying a certain thrill of pleasure in rough justice (which of us wouldn't like to slay a litter lout?) it speaks to the quiet majority.

But after that strong opening, one senses the film casting about for ideas, not certain of its tone or direction. The ending arrives so randomly one wonders if the ideas did run out and Wheatley just called it a day. Bobble hats off, all the same, to Alice Lowe and Steve Oram as the least glamorous pair of killers ever to be seen on the loose, and to Eileen Davies, whose keening lament for her deceased dog is the first sound we hear in the picture – and a suitable prelude to the barking madness that follows.